On the Feigenbaum-CvitanoviĆ equation in the theory of chaotic behaviour

Abstract

We propose an analytic perturbative approach for the determination of the Feigenbaum-CvitanoviĆ function and the universal parameter α occurring in the Feigenbaum scenario of period doubling for approach to chaotic behaviour. We apply the method to the case Z=2 where Z is the order of the unique local maximum of the nonlinear map. Our third order approximation gives α=2·5000 as compared to "exact" numerical value α=2·5029 ... We also obtain a reasonably accurate value of the Feigenbaum-CvitanoviĆ function.